Kamel Barkaoui

A deadlock prevention method for a class of FMS

In this paper we propose a deadlock prevention method for a class of FMS called System of Simple Sequential Processes with Resources (S/sup 3/PR). This method is based on structural theory of Petri nets and it is composed by two phases. The first phase adds local control places to the S/sup 3/PR net such that all uncontrolled siphons of the S/sup 3/PR net become controlled. We then obtain the augmented S/sup 3/PR net. When deadlock-freeness of the augmented S/sup 3/PR net is not guaranteed, we modify initial markings of local control places. Thus, we obtain the controlled S/sup 3/PR net. We demonstrate that the controlled net cannot reach a dead-marking and by exploiting its structure, we state its liveness.

Supervisory control of discrete event systems based on structure theory of Petri nets

The present work is related to the use of Petri nets structural techniques in the supervisory control of discrete event systems. A relevant property of the system behaviour under supervision is to be non-blocking, i.e. from any state reachable from initial state, it is always possible to reach a desirable (or marked) state. Recent works had shown that the synthesis of proper supervisors based on Petri net modelling of DES is an interesting approach. In this paper, we present a proper supervisor synthesis method based on a purely structural reasoning. This parametrized method is especially well-suited for a large class of discrete event systems, called G-Task, for modelling concurrent automated manufacturing systems with flexibility on routings and on synchronization patterns with shared resources. Also, it can be exploited for enforcing constraints on the reachability set of any bounded uncontrolled net.

On Liveness and Controlled Siphons in Petri Nets

Structure theory of Petri nets investigates the relationship between the behavior and the structure of the net. Contrary to linear algebraic techniques, graph based techniques fully exploit the properties of the flow relation of the net (pre and post sets). Liveness of a Petri net is closely related to the validation of certain predicates on siphons. In this paper, we study thoroughly the connections between siphons structures and liveness. We define the controlled-siphon property that generalizes the well-known Commoners property, since it involves both traps and invariants notions. We precise some structural conditions under which siphons cannot be controlled implying the structural non-liveness. These conditions based on local synchronization patterns cannot be captured by linear algebraic techniques. We establish a graph-theoretical characterization of the non-liveness under the controlled-siphon property. Finally, we prove that the controlled-siphon property is a necessary and sufficient liveness condition for simple nets and asymmetric choice nets. All these results are illustrated by significant examples taken from literature.

New Petri Net Structure and Its Application to Optimal Supervisory Control: Interval Inhibitor Arcs

This paper presents a new Petri net structure, namely, an interval inhibitor arc, and its application to the optimal supervisory control of Petri nets. An interval inhibitor arc is an arc from a place to a transition labeled with an integer interval. The transition is disabled by the place if the number of tokens in the place is between the labeled interval. The formal definition and the firing rules of Petri nets with interval inhibitor arcs are developed. Then, an optimal Petri net supervisor based on the interval inhibitor arcs is designed to prevent a system from reaching illegal markings. Two techniques are developed to simplify the supervisory structure by compressing the number of control places. The proposed approaches are general since they can be applied to any bounded Petri net models. A marking reduction approach is also introduced if they are applied to Petri net models of flexible manufacturing systems. Finally, a number of examples are provided to demonstrate the proposed approaches and the experimental results show that they can obtain optimal Petri net supervisors for some net models that cannot be optimally controlled by pure net supervisors. Furthermore, the obtained supervisor is structurally simple.

Theoretical Aspects of Computing - ICTAC 2006

Invited Papers.- Verifying a Hotel Key Card System.- Z/Eves and the Mondex Electronic Purse.- Verification Constraint Problems with Strengthening.- Semantics.- Quantitative ?-Calculus Analysis of Power Management in Wireless Networks.- Termination and Divergence Are Undecidable Under a Maximum Progress Multi-step Semantics for LinCa.- A Topological Approach of the Web Classification.- Concurrency.- Bisimulation Congruences in the Calculus of Looping Sequences.- Stronger Reduction Criteria for Local First Search.- A Lattice-Theoretic Model for an Algebra of Communicating Sequential Processes.- A Petri Net Translation of ?-Calculus Terms.- Model Checking.- Handling Algebraic Properties in Automatic Analysis of Security Protocols.- A Compositional Algorithm for Parallel Model Checking of Polygonal Hybrid Systems.- Thread-Modular Verification Is Cartesian Abstract Interpretation.- Formal Languages.- Capture-Avoiding Substitution as a Nominal Algebra.- Prime Decomposition Problem for Several Kinds of Regular Codes.- A New Approach to Determinisation Using Bit-Parallelism.- Logic and Type Theory.- Proving ATL* Properties of Infinite-State Systems.- Type Safety for FJ and FGJ.- Partizan Games in Isabelle/HOLZF.- Proof-Producing Program Analysis.- Real-Time and Mobility.- Reachability Analysis of Mobile Ambients in Fragments of AC Term Rewriting.- Interesting Properties of the Real-Time Conformance Relation tioco.- Model Checking Duration Calculus: A Practical Approach.- Spatio-temporal Model Checking for Mobile Real-Time Systems.- Tutorials: Extended Abstracts.- Tutorial on Formal Methods for Distributed and Cooperative Systems.- Decision Procedures for the Formal Analysis of Software.

On the enforcement of a class of nonlinear constraints on Petri nets

This paper deals with the enforcement of nonlinear constraints on Petri nets. A supervisory structure is proposed for a class of nonlinear constraints. In order to enforce a nonlinear constraint on a Petri net, we propose a transition transformation technique to replace a transition in an original net by a set of transitions. Then, a control place is designed to control the firing of these transitions, aiming to enforce the nonlinear constraint. The proposed supervisor is maximally permissive in the sense that it can make all markings in the admissible-zone reachable and all markings in the forbidden-zone unreachable. The proposed method is applicable to bounded Petri nets. Finally, a number of examples are provided to demonstrate the proposed approach.

A Polynomial-Time Graph Algorithm to Decide Liveness of Some Basic Classes of Bounded Petri Nets

This paper is related to structural analysis of Petri nets where liveness and boundedness issues are addressed through the analysis of the combinatorial properties of the underlying graph. We first recall a number of basic results about liveness and boundedness involving combinatorial substructures (deadlocks and traps). It is then shown that testing whether a bounded Extended Free Choice net or a Non Self-Controlling net is structurally live can be reduced to the search for a strongly connected deadlock which is not a trap. This problem, in turn, is shown to be solvable in polynomial time through a purely combinatorial algorithm making combined use of Tarjans strong connectivity algorithm and Minouxs LTUR algorithm for solving Horn satisfiability problems. Once structural liveness has been proved, testing liveness for a given initial marking is already known to be polynomially solvable.

Compact Supervisory Control of Discrete Event Systems by Petri Nets With Data Inhibitor Arcs

This work proposes a novel structure in Petri nets, namely data inhibitor arcs, and their application to the optimal supervisory control of Petri nets. A data inhibitor arc is an arc from a place to a transition labeled with a set of integers. A transition is disabled by a data inhibitor arc if the number of tokens in the place is in the set of integers labeled on it. Its formal definitions and properties are given. Then, we propose a method to design an optimal Petri net supervisor with data inhibitor arcs to prevent a system from reaching illegal markings with respect to control specifications. Two techniques are developed to reduce the supervisor structure by compressing the number of control places. Finally, a number of examples are used to illustrate the proposed approaches and experimental results show that they can obtain optimal Petri net supervisors for the net models that cannot be optimally controlled by pure net supervisors. A significant result is that the proposed approach can always lead to an optimal supervisor with only one control place for bounded Petri nets on the premise that such a supervisor exists.

On Liveness in Extended non Self-Controlling Nets

For several years, research has been done to establish relations between the liveness of a net and the structure of the underlying graph. This work has resulted in the proposition of polynomial algorithms to check liveness for particular classes of nets. In this paper, we present Extended Non Self-Controlling Nets, a class of nets that includes Extended Free-Choice Nets and Non Self-Controlling Nets. We develop some properties of this new class of nets and we propose polynomial algorithms whose application domain is wider than the domain of the previous algorithms.

On the equivalence between liveness and deadlock-freeness in petri nets

This paper deals with the structure theory of Petri nets. We define the class of P/T systems namely K-systems for which the equivalence between controlled-siphon property (cs property), deadlock freeness, and liveness holds. Using the new structural notions of ordered transitions and root places, we revisit the non liveness characterization of P/T systems satisfying the cs property and we define by syntactical manner new and more expressive subclasses of K-systems where the interplay between conflict and synchronization is relaxed.